Mary's age is twice her brother's age and half her sister's age. How old is Mary, in years, if the sum of the three ages is $28$ years?
Explanation: If $m$, $s$, and $b$ represent the respective ages of Mary, her sister, and her brother, we have $m=2b=\frac{1}{2}s$. We multiply all terms by $2$ to get $2m=4b=s$. We now have $m$ and $s$ in terms of $b$, so we can substitute them into the equation $m+s+b=28$. $$2b+4b+b=28 \Rightarrow 7b=28 \Rightarrow b=4$$ If her brother's age is $4$, then Mary is $2b=\boxed{8}$ years old.